It’s not everyday that a newly discovered 3-D mathematical concept appears on the topological horizon. But one did in 2012. It’s called the Bamboozle Structure.
“Bamboozle consists of 51 equilateral triangles, meeting pairwise at an angle of about 70.5 degrees (arccos 1/3).”
It seems that topologists haven’t given a great deal of consideration to Bamboozle Structures since their discovery, but Timo Scholte (Eindhoven University of Technology, The Netherlands) is an exception.
“Since bamboozle structures are a relatively new concept that have so far strictly been viewed as single orbits under space groups, there are still possibilities to improve our understanding of such structures. In this thesis, we relate bamboozle structures to tessellations of three dimensional Euclidean space, namely convex uniform honeycombs. This is done by relating the problem to its two dimensional equivalent, identifying what convex uniform honeycombs hold (near-)bamboozle structures, proving of completeness of the list of used convex uniform honeycombs with the help of computer calculations, and considering what adjustments convex uniform honeycombs can withstand in order to create bamboozle structures. Though the search for new bamboozle structures proved unfruitful, we found that the hexagonal bamboozle structure was in fact not a bamboozle structure, discovered that the square bamboozle structure and the four-coloured rectangular bamboozle structure actually form continuous families, and gained a better understanding of the bamboozle structure and what areas should be considered to find a complete list of possible structures.”